Physics, 02.09.2019 23:10 randenbrown1653

For this example, let
$m_a and m_b$ are masses
l₁, l₂, l₃ and x be lengths
t₁ and t₂ be times
a mass density is defined as mass per volume, and a volume has a dimension of [l]³. which of the following could be mass densities?
a. $\frac{m_a. m_b}{l_1.l_2}$
b. $\frac{m_a}{l_1^2.l_2^2}.x[/tex ]br / c. [tex]\frac{l_1.l_2.l_3}{m_a}$ < br /> d. $\frac{m_a}{l_1.l_2.\frac{x}{t_ 1}t_2}$

Answers: 1

Show answers

Answers

Answer from: chrisraptorofficial

The answer can be b $\frac{m_{a} }{{l_{1}}^{2}.{l_{2}}^{2}}.x$ i

or d. $\frac{m_{a} }{l_{1}.l_{2}.\frac{x}{t_{1}}.t_{2}}$

Explanation:

As the question says the mass density has units of mass per volume, that means that when you have numbers, this will have units so when you realice the all the operations of the equation the units that the number must have should be $\frac{Mass}{Lenght^{3} }$ .

To get to this result you have to take into account the properties of exponents.

- If you have the same base, and the varibles are multiplying you have to add the exponents for example:

mass x mass each mass has exponent one so you add the exponents (1+1=2) at the end you will have $mass^{2}$ .

- If you have the same base, and the variables are dividying you have to substract the exponents for example:

$\frac{time}{time}$ , each time has exponent one so if you substract (1-1=0) at the end you will have $time^{0}$ . In this case there is an other property that say that when you have any number with exponent cero that number becomes one so $time^{0}$ = 1.

- If we have a negative exponent it means that it must be in the lower part (divisor) of the division for example:

$x^{-2}= \frac{1}{x^{2}}$

Now coming back to the problem we are going to realice each one of the process of the equations to determine which of it fulfills the requirements for mass density remember at end we should get $\frac{Mass}{Lenght^{3} }$ units.

- a) $\frac{m_{a}.m_{b}}{l_{1} .l_{2}}$

In this answer we multiply ma x mb so at the end the units of the upper(dividend) part must be $m^{2}$

In the lower part (divisor) we must multiply l1xl2 so we will have units $l^{2}$

So at the end the units for a option are: $\frac{m^{2} }{L^{2}}$ which doesn't correspond with the mass density units.

- b) $\frac{m_{a} }{{l_{1}}^{2}.{l_{2}}^{2}}.x$

First in the dividend we must multiply ma with x so the units will be m.L because they dont have the same base so we can´t add them

After that we will multiply in the divisor ${l_{1}}^2.{l_{2}}^2$ so as the exponents are 2 we will have 2+2 this is 4. So we will have $L^{4}$

At the end we will have the following units: $\frac{m.L}{L^{4}}$ we have L in both the uper and lower part as we have the same base we can substract 1-4 = -3 as it is a negative number it must be in the divisor so at the end we will have the followind expresion:

$\frac{m}{L^{3}}$ that has the units of mass density

- c) $\frac{l_{1}.l_{2}.l_{3}}{m_{a}}$

First in the dividend we have to multiply l1xl2xl3 so for calculating the units we have to add all the exponents because they are multiplying and have the same base so l1xl2xl3 = $l^{1+1+1}=l^{3}$

The units in the divisor remain in the same way because they doesn't have any operation so we will have mass units s

At the end the units of this expresion will be: $\frac{l^{3} }{m}$ it is the oposite to what we need to have mass density units so this is not the correct answer either

In this moment we have already discard the other options so we know the answer is d but here it comes the explanation

- d) $\frac{m_{a} }{l_{1}.l_{2}.\frac{x}{t_{1}}.t_{2}}$

In this case we have in the dividend mass units so we leave it like that

For the divisor we are going to take all the units and multiply them so remember that l1, l2, l3 and x have length units that we will represent with an L and t1 and t2 have time units that we will represent with a t. So if we replace with the units in the dividend we will have the following expresion }(remeber in this moment we are just going to work with the lower part of the expresion):

$l_{1} .l_{2} .\frac{x}{t_{1} } .t_{2} = L.L.\frac{L}{t}.t\\$

As you can see we have 3 lenghts that are multyplying so we have the same base we have to add the exponents = $L.L.L = L^{1+1+1} = L^{3}$

But we still have time so the expresion in this point is $\frac{L^{3}.t }{t}$ we have two times that are dividying so the operation will be

$\frac{t}{t} = t^{1-1} =t^{0}=1$

At the end we will have: $L^{3}.1 = L^{3}$

Now remember that we were working just with the divisor so as we take into account the mass unit of the dividend the expresion will be:

$\frac{m}{L^{3}}$

So you have with this expression mass density units

Answer from: Quest

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

Answer from: Quest

490 n

f=125n a=2.5m/s2

Another question on Physics

Physics, 21.06.2019 14:10

Amachinist needs to remove a tight fitting pin of material a from a hole in a block made of material b. the machinist heats both the pin and the block to the same high temperature and removes the pin easily. what statement relates the coefficient of thermal expansion of material a to that of material b? a) the situation is not possible, heating block b will shrink the hole in the material as the material expands with increasing temperatureb) material b has the same coefficient of expansion as does material ac) material b has a negative coefficient of expansion and a has a positive coefficient of expansiond) material a has a greater coefficient of expansion than does material be) material b has a greate

Answers: 1

Answer

Physics, 22.06.2019 11:20

Sound is a disturbance that travels through a medium as a

Answers: 1

Answer

Physics, 23.06.2019 01:30

Lacie kicks a football from ground level at a velocity of 13.9 m/s and at an angle of 25.0° to the ground. how long will the ball be in the air before it lands? round your answer to the nearest tenth. s how far will the football travel before it lands? round your answer to the nearest tenth. m

Answers: 3

Answer

Physics, 23.06.2019 01:50

Aseries circuit contains a 30 e resistor, a 20 resistor, and a 10 resistor. the power supply provides 100 v to the circuit the current in the 10 resistor, to two significant figures, is a.

Answers: 1

Answer

You know the right answer?

For this example, let
[tex]m_a and m_b[/tex] are masses
l₁, l₂, l₃ and x be lengths

Questions